# Absolute vs. Relative Difference in Survival Time - Is this possible?

So there's a fairly well characterized difference between relative risk and absolute risk for conventional cohort studies, and for many questions, the absolute risk is arguably more appropriate.

Is there an analogous way to measure absolute difference for accelerated failure time models? I suspect there isn't, because these models assume proportional survival times, so the relative measure will be constant, but the absolute measure will vary over time, but I wanted to make sure before I abandoned this line of reasoning.

Would it be possible to do it at a fixed point in time, say the median - and do you think this would be of any value?

• Just to clarify my understanding: absolute risk of disease is a risk of experiencing an event over a specified interval conditional upon not dieing from other causes (ranges from 0 to 1), whereas the relative risk is a comparison of risks under two different settings (ranges from 0 to $\infty$). Further, the criticism of relative risk is a tendency to exaggerate the deleterious effects of exposures for extremely rare diseases, e.g. a 100-fold risk ratio for a less than 1/1,000,000 incidence is practically negligible. Is this correct? – AdamO Jan 3 '18 at 19:03

Risk ratios and risk differences are two different measures of association for time-to-event outcomes as observed in cohort studies. Risk ratios are the most commonly presented type of outcome because they are easily estimated from Poisson, logistic, or Cox proportional hazards models. Risk differences, or the difference in absolute risk, while less common, boasts several advantages over the risk ratio in terms of interpretability. For instance, if a 50 year old non-smoking woman's 10 year CVD death risk is 1 (10 events per 1,000 person years) whereas a counterfactually matched 50 year old smoking woman has a 10 year CVD death risk of 2% (20 events per 1,000 person years) the risk difference is 1% but the risk ratio or relative risk is 2 or 100%; people often conflate percentages in this case as a fraction of events to person years $\times 100$ (absolute risk difference) or as a proportional difference (RR1/RR2: unitless).